Problem: Solve for $x$ and $y$ using elimination. ${3x-6y = -39}$ ${5x-5y = -30}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-5$ and the bottom equation by $3$ ${-15x+30y = 195}$ $15x-15y = -90$ Add the top and bottom equations together. $15y = 105$ $\dfrac{15y}{{15}} = \dfrac{105}{{15}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {3x-6y = -39}\thinspace$ to find $x$ ${3x - 6}{(7)}{= -39}$ $3x-42 = -39$ $3x-42{+42} = -39{+42}$ $3x = 3$ $\dfrac{3x}{{3}} = \dfrac{3}{{3}}$ ${x = 1}$ You can also plug ${y = 7}$ into $\thinspace {5x-5y = -30}\thinspace$ and get the same answer for $x$ : ${5x - 5}{(7)}{= -30}$ ${x = 1}$